Problem: Simplify the following expression: $ y = \dfrac{-2t - 8}{6t + 8} - \dfrac{-9}{2} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-2t - 8}{6t + 8} \times \dfrac{2}{2} = \dfrac{-4t - 16}{12t + 16} $ Multiply the second expression by $\dfrac{6t + 8}{6t + 8}$ $ \dfrac{-9}{2} \times \dfrac{6t + 8}{6t + 8} = \dfrac{-54t - 72}{12t + 16} $ Therefore $ y = \dfrac{-4t - 16}{12t + 16} - \dfrac{-54t - 72}{12t + 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-4t - 16 - (-54t - 72) }{12t + 16} $ Distribute the negative sign: $y = \dfrac{-4t - 16 + 54t + 72}{12t + 16}$ $y = \dfrac{50t + 56}{12t + 16}$ Simplify the expression by dividing the numerator and denominator by 2: $y = \dfrac{25t + 28}{6t + 8}$